In the spirit of full disclosure I have a history knowing/liking one of the owners of Backyard Pizza and I am friends with the family of the other owner. On the flip side the guy running Pub and Oven (the place next door to Backyard) has done somethings before the pizza business that have really impressed me and I respect him.
Ok, with that out of the way I'm going to compare and contrast the two joints. It's enivitable considering they are literally right next door, both are pizza places, and both seem to be focusing on the idea of pizza and beer. This won't be a comprehensive comparison becuase I have only had one pizza at the Pub and Oven and I've not seen their beer selection yet.
Atmosphere
Backyard Pizza is a dark place with shoddy air conditioning. The furniture, wall decorations, and lighting are all pretty cool and the whole vibe, minus the air conditioning, is pretty cool. I especially dig the lights which are pretty creative. I also like that they feature local art on their walls (and that the art is for sale). The use of birch trees to segment the space is something I particularly like. Finally the bar is really cool looking and it is easy to see the beer taps from almost any seat in the main dining area. Along with the bad air conditioning the smoke from the oven is a real deterrant as I don't really like smelling of smoke when I leave the place.
Pub and Oven on the flip side is very wide open bright and airy. It has a very polished and professional feel but is lacking the intamcy of Backyard Pizza. The colors are all bright without being garish. Even though the space is very open and tall it avoids feeling like you are in the middle of a cafeteria because of the colors, the relatively small size of the actual room, and the pillars that sprout around the dining area. The air conditioner is working perfectly and there is no smokiness to the restaurant. I definitely prefer the ambiance of Backyard but mostly because it is different without being tacky.
Pizza
This is where it's really at - I mean, what's a comparision without taking about their respective pizzas. So far, based on my limited exposure to Pub and Oven, I vastly prefer the pizza I've had at Backyard.
I've had a variety of Pizza's at backyard. I've had the jamacian jerk chicken, the memphis bbq, the sunspot, the pepperoni, and the tuscany. They were all pretty good pizza's and I especially liked the sunspot. Here is a pdf of their menu so you can get a description of each of the pizza's I've mentioned. The crust is thin but not quite NY thin and the flavor balances on each pizza has been pretty darn spot on. Backyard isn't my favorite pizza ever but it certainly gives Huntington a step in the right direction towards tasty pizza (La Famigla is also pretty good).
At the Pub and Oven I've just had their Chipotle Chicken pizza and, quite frankly, it was a let down. As I told the manager (owner?) today I thought it would be better with red onions instead of white, it could use a little less garlic (or at least have the garlic spread out more and not just clumps of cloves), and it could probably use a tangier sauce. The chicken itself was mostly flavorless and the white onions were mostly just gooey. The only really prominent flavor on the pizza was the garlic.
My friend John had the Hawaiin pizza (applewood smoked bacon and pinapple) and he said it was very good. One other patron also raved about the Hawaiian while another friend had the Italian Mafia and said it was nothing he couldn't have just made at home.
Service
Service at both is decent. I think they will both be OK though I think that Pub and Oven gets the nod here; not because their service is better but becasue they aren't having to fight with thier point of sale (POS) system. Backyard is using some kind of iPhone/iPad dongle and it just hasn't been consistently reliable. Pub and Oven is using a standard POS terminal and they had no problem processing our order.
Both are a little slow - but it's hard to complain about that considering they are making a pizza fresh to order for you and they are both very new. I imagine they will both improve at their speed in the future.
Price
Well, Backyard wins this hands down only becuase they have more variety of ways to get their pizza at various price points. Every pizza at Pub and Oven could only be ordered in either a 10" or 16" size and the prices were typically about $12 for the ten inch and $22 for the 16 inch. Basically, after a soda and a 10" pizza I had a $15 lunch tab. That's tough to justify.
Backyard also has fairly expensive pizza and their large is only a 14". However, they also sell some pizza's by the slice at $2.50/slice which means you can get a decent lunch of two slices and a soda for about $7.50. That's half the price. I only ate half of my pizza at Pub and Oven (took the other half with me) but I only wanted half a pizza worth (10"). I don't really have a lot of use for half a pizza that I didn't particularly like.
Summary
At the moment I am definitely a bigger fan of Backyard pizza. I do wish they would fix their AC and maybe install some better ventilation so I don't end up smelling like smoke after a meal. But for both lunch and dinner I like their pizza, and their serving sizes, better.
I'll go back to Pub and Oven and try a different pizza (I wish they had their menu online) but I'll probably do so for dinner where I can share a pizza becuase I can't afford to eat there for lunch on even an occassional basis.