The original is definitely a better game for at least three reasons:
1) As Wario notes, the original is a much faster-paced game. This is Overkill's fault, because it was produced for home consoles rather than arcades. This is obvious in both the gameplay and the incredibly long cinematics.
2) The design in the original was much, much more varied and vibrant. Here the bosses are basically just a bunch of typing, like the rest of the levels. In the original each boss had a theme (the best is the boss that asks you philosophical questions and offers you multiple choices to respond to it). The original had segments where you stopped and fought onslaughts of zombies in a challenge type format. The challenges all had themes. Powerups reduced the difficulty in novel ways, where here there's just a slowdown.
3) The original had the characters wearing Dreamcasts and holding keyboards, which is so silly but so fun. This reflects that the original was developed by Sega as a retail product supporting a peripheral and their overall hardware vision, whereas this is a small project done by an indie team. I'm very glad that this project has a space to exist and I know the original is sort of a weird thing that could never happen again, but it is what it is.
But this is still a great game and if you have fond memories of the original and want to play a new Typing of the Dead, you definitely want this. $8 is an excellent launch price. Seriously, pick it up.
I hope Sega does release some interesting DLC dictionaries but more importantly opens up the dictionary format to modding. Given that leaderboards show people using UK and US English, I suspect the dictionaries are encrypted for leaderboard security purposes. Which is a bummer, because I'd love to work on cracking the format but if it's something that would ruin the competitive layer of the game that'd be really too bad.
You have to type spaces (unless that's just added on Motherfucker difficulty). Also, if you screw up a word, it resets and changes to a new one.
Capitals are never required from what I've seen so far.
You do not need to type spaces in either the original or this game (although you may find it helpful because you get a word that ends with a letter followed by another word that starts with the same letter and without using a space this could trip up your flow). You do need to type apostrophes and hyphens. You do not need to type capitals.