Frankly if anybody wanted a half way decent Hellsing game lords of shadow 2 aint a bad choice
https://youtube.com/watch?v=gKsEPoJMuKY
Pros: replicates the feeling of being an unstoppable killing machine that becomes progressively more powerful and unstoppable. Good level design and interesting plot. You eat people and Fight the devil
Cons: mandatory stealth sections. It makes sense early on ( you've just woken up a thousand years after being drained of blood and chaos space marines are after your ass) but it's pushed past the point of enjoyment. Also the final boss is decent but extremely short and underwhelming.
I like how the TV series plays up the horror and otherworldliness. It goes knee deep into the procedural aspects too, and I enjoyed the increased focus on hellsing's power and limitations. The biggest shock was seeing how good the animation looks in HD. It looks less cheap and more artistic when upscaled.
Frankly the whole product was good enough on its own that I wouldn't have minded a second season. Probably the only anime I can think of that actually pulled off an original conclusion when they didn't have any more creator material to work with.