1. Grammar - Vietnamese grammar is not particularly any more difficult than to Chinese (Mandarin), but I feel as if there are many exceptions to those rules being taught in the language courses. For example, if you wanted to say:
eg. (Because) he was drunk, (therefore) I had to take him home.
You could say:
Vì anh ấy bị sỉn rượu, tôi phải chở anh ấy về nhà.
But you could get rid of vì, or add tại or bởi infront of it. Also, you can remove bị, rượu and nhà altogether and it would still make sense. If you take away vì, you must add either cho nên, vì thế or sở dĩ...etc.
2. Pronunciation - If you compare Vietnamese pronunciation with Chinese (Mandarin), I think you'd agree that the Standard Vietnamese (Northern) pronunciation is quite hard enough to master, let alone the Southern or Central dialects. There are 6 tones in Standard Vietnamese and 5 in most of the others. The tones vary from extreme to extreme. The hardest tone to master is the ngã (~) tone. Even the Southerners have merged this into the hỏi (?) tone. Tone Sandhi thankfully does not occur in modern Vietnamese although there are traces of this in words such as cảm ơn/cám ơn (thank you).
3. Reading and writing - If you compared today's writing systems, then Chinese would be far ahead for obvious reasons. The Vietnamese script nowadays is 90-95% phonetic. If, however, you compare Chinese with Chữ Nôm.
- Firstly, in order to even read a Nôm character, you would have to learn at least 3000 Chinese characters to be moderately literate. Of course, many of those characters mightn't even be used that often. Each of the characters has a corresponding Vietnamised reading known as Hán-Việt (Sino-Vietnamese). However, that just covers the Sino-Vietnamese words in Vietnamese (which do account for up to 60% of all words). What about the ordinary speech? In ordinary speech, Vietnamese still use between 20-30% Chinese vocabulary without realising it. For those other 70-80% of native Vietnamese words, they must be transcribed using Chữ Nôm. But things aren't so simple.
- The Vietnamese phonology is similar but not an exact replica of that of Chinese. Therefore, there are many native words which do not have an exact Sino-Vietnamese (Hán-Việt) reading. As a result, the people who created Chữ Nôm used "rough borrowings of sound". In other words, for those sounds that were present in Vietnamese but not in Chinese, they used similar sounds to do the job. Note also that Chữ Nôm combines: original Chinese characters with their exact pronunciations and meanings (Hán-Việt), original Chinese characters with a phonetic pronunciation and invented characters (Nôm).
- An example is the character 竜 which is an old simplified form of the word dragon (龍). 竜 in Hán-Việt is pronounced 'long' and of course means dragon. However, 滝 is pronounced sông (river), [竜+內] is pronounced trong (inside) and [竜+目] is pronounced trông (clear). So just with those characters, you can see that the phonetic element is used mostly for its medial and final sound. Of course, there are many more examples of this. However, what about the historic pronunciations? Actually during the medieval period, sông was pronounced somewhat like klông, and trong/trông were like tlong/tlông. As you can see, the long/lông is actually there - the modern pronunciations just conceal that. Some Nôm characters have phonetic components which are merely used for their medial or final sound. Of course, Vietnamese like most languages has changed a lot since the medieval ages.
- As I mentioned just above, some original Chinese characters are used simply as phonetic characters such as 女 can be read in Hán-Việt as nữ (female) or in Nôm as nữa (moreover, furthermore, also).
- I could go on, but as you can see, the Hán-Nôm writing system is not as simple as it sounds. It combines Chinese characters with their original pronunciations and meanings, Chinese characters used for phonetic purposes to represent a native Vietnamese sound, invented characters (mostly using a semantic and phonetic component) and phonetic borrowings off invented characters. Also, just as you may notice in modern Chinese, the modern Vietnamese pronunciations of certain characters with the same phonetic component is not always the same. This is obviously due to sound change, and semantic phonetic characters are a bit harder to learn because you'd need a fairly good understanding of Chinese characters and their Vietnamised pronunciations.
Ok, I should stop here. All I wanted to say was that Chữ Nôm would be harder to learn - not because the average character has more strokes, but because it combines three different types of characters; original Chinese character (w/ original meaning) but pronounced with a nativised pronunciations (Hán-Việt), original Chinese character (used phonetically to represent a native Vietnamese syllable), and an invented Vietnamese character. Also factor in the fact that although most Chữ Nôm characters are available to view online and many have been encoded into Unicode, there has never been a full standardisation of Nôm characters, and even today, people can use their own variant of a character, and finally factor in the fact that there are modern words with no existing character but can be represented using an existing one.
And yes, Classical Chinese will help you. With regards to original texts, most texts were written in Classical Chinese but there are many that were written in Chữ Nôm. These Chữ Nôm texts for the most part follow modern Vietnamese syntax but use a lot of odd and no longer used native expressions. Japanese writing sounds like a mess! All sounds in modern Vietnamese may be represented in Chữ Nôm. To be considered "literate" you should aim to learn 3,000-5,000 Chinese characters, and about 3,000-5,000 native characters (~6000-10,000).

Me and a few others are currently transcribing texts for fun, but also aim to do our own standardisation for ourselves. Oh and the average Vietnamese in an informal situation will only speak 15-20% words of Chinese origin, everyday Vietnamese would have about 20-30% Chinese (or Japanese) derived vocabulary and in formal contexts, the media etc. then you can expect the amount to be 50% at the least and even higher (as much as 80%) in essays and documentation.