Wow, great question. I answered that I like both equally well but for many different reasons.
First of all, they BOTH greatly influenced me to serve and deploy to combat with the 101st Airborne Division, which has an amazingly rich history. In SPR, of course Private Ryan and several other supporting cast (including Ted Danson's character with the 101st Pathfinders) were members of the 101st and they fought hard in the last part of the movie. In BoB, of course, the entire series follows what is now 4th Brigade of the 101st (Currahee). I have accomplished a lot of goals, including having served with 3rd BCT 101st on my first combat tour in Iraq. I owe some of that, oddly, to Hanks and Speilberg (quite anti-war I believe) but not so oddly to those men that fought and also gave interviews on BoB.
SPR is about 2.5 hours, 1/4 the length of BoB and therefore has to fit more character development and action in much less time. SPR is arguably the best war movie of all time. It's believable, lacks the unrealistic scenes that scar many war movies (shooting from the hip, dumb dialogue, bad effects, 'hero' characters, etc.). It's scary realism from start to end. And the characters are very real and human. Five stars.
BoB is a 10 hour miniseries. I'm a paratrooper (another goal partly as a result of the BoB series), so it's very close to my heart. I have such appreciation and admiration for those brave men that jumped into Europe. Those scenes are so chilling to me. The character development is also top shelf. War scenes are very real, but with a longer series there are more mistakes (albeit all quite minor mistakes). The characters are very real and human too. Some episodes focus on one or two characters, which is really cool. Top shelf too, and 5 stars.
Both are great investments to own. I've watched both many times. For a few bucks you can own the two best movies ever.
The other two fantastic ones in my book are Platoon and Full Metal Jacket and Black Hawk Down.