They are completely different experiences like night and day however depending on what you're looking for they are both good places. I normally dive with Aldora but I also run group trips through my dive shop with Scuba Club Cozumel.
In a nut shell, I find Scuba Club Cozumel to be more of a "no-frills" type of dive vacation where Villa is bit more upscale. I consider the rooms to be more like mini condos. The beds in the Villa are extremely comfortable, small kitchenette (larger rooms have full kitchens where smaller ones have microwaves/coffee maker) allows you to go shopping and make your own meals. The grounds and rooms in the Villa are kept immaculately clean. Seriously I never see them stop cleaning. While there is no on-site bar or restaurant at the Villa but you'll find most guests are happy to sit under the palapa and share cervezas.
Scuba Club Cozumel is more of a "dive budget" type resort. The rooms are large, clean but very basic. The beds are simply a firm mattress pad on a concrete slab. Works well for me since I like a firm mattress. Small refrigerator, no TV, no phone, not that many electrical outlets in room. The resort will be much more crowded than the Villa. I find the Villa to be more relaxing and a bit more private. Villa has 13 rooms whereas SSC has many more. Both SSC and Aldora Villa have nice balconies if you get one overlooking the water.
The diving in front of Scuba Club Cozumel is a macro paradise for photographers and a great place to do refreshers, night dives, and long shore dives. While it's mostly debris / rubble I've had some great shore dives in front of Scuba Club Cozumel. The on-site dive shop allows you to sign out a tank (make you do this before they close for the day) and go diving anytime you like. The Villa usually also has tanks available for shore diving but I'd give a slight edge to the diving in front of Scuba Club Cozumel.
Scuba Club Cozumel has an "semi" all-inclusive package that includes 3 meals a day. This can be great if you're trying to save money. I found the food to be so-so. Nothing was bad but nothing was particularly excellent to me. I wasn't a fan of their breakfast but lunch and dinner options were usually good. It's not a buffet style, you order the meals in advance. The service was good once you get to know the waiters.
Distance wise, Scuba Club Cozumel is "slightly" closer to downtown. I would say the Villa is about 5-10 minutes further away from town than SSC but both are walk-able if you like walking. Scuba Club Cozumel takes about 15-20 minutes to walk into town while the Villa is closer to 25-30 minute walk. Both should be less than a 40-50 peso (2.20USD-2.80USD) taxi ride into town. The Villa provides free usage of bicycles to go into town. Scuba Club Cozumel is about 10 minute walk to Mega / Chedrau for grocery shopping. Usually the Villa manager will take guests via truck to Mega to go shopping.
The diving at Scuba Club Cozumel is your typical Caribbean cattle boat. Nothing wrong with it at all but they are your fairly typical Cozumel dive operator. Good divemasters but your dives are fairly regimented. Slow boats with 12+ divers and standard AL80s. Most dives are between 45-60 minutes depending your group's air consumption. If you have a good group it will be closer to 60 minutes. It will take a long time to get to some of the sites that are further south. We had to "negotiate" with them to take us to Colombia or even Palancar Caves. Forget about Maracaibo or Punta Sur.. Again, your dive experience with Scuba Club Cozumel will largely depend on the experience and comfort level of everyone on your boat. They do a good job of trying to split up groups by experience level when they can.
In contrast, Aldora has much smaller groups (usually no more than 6-7 people) and faster boats. Steel HP100 and HP120s for longer dives. Average dives are generally 70-80 minutes. More personalized service and longer dives. They stop at beach club for your surface interval to allow you to buy food if you want.
They will go to further or in some cases less frequented dive sites that some other dive operators will avoid due to fuel costs and slow boats. There is no having to "negotiate" with them to go to further sites provided everyone in your group is experienced.