Decision Time> To what use will the basement be put ??
How much room can you spare ?
What kind of soil surrounds the basement??
I would not use either contractor, good ones will never badmouth their competition.
If you are really lucky, maybe you can discover a decent engineer who is expert at these problems.
Also talk to the neighbors, maybe they have had similar problems and know of a solution.

I also had a problem with water in the basement. The firm I had do the work drilled up the floor for a few inches wide next to the wall where the water was coming in. They installed drainage tile which drained to a sump pump. This solution was one of the cheaper estimates and it is working fine. No more puddles of water on the floor since I had it done a couple of years ago.

Abby

If the water is coming up from under the floor, then the under floor solution is preferable (but more expensive).

The conduit type things at the base of the wall will collect the water. They will also grow mildew and stink. The basement will always have that 'damp basement' smell because, well. it is a damp basement. Get the water before it gets in. If the gravel bed under the slab is good, only a single pump pit may be required. It can even be sealed to prevent smells from getting in.

I've worked on similar problems many times. The sump pump fix will probably work but why put your faith in a pump that could fail or be subject to a power outage. If you have a low point on the property that is below the footing in elivation I would dig out the foundation from the outside and install a 4" drain around as much of the foundation as possible. I would then gravity feed it to the low point. Of course this is only possible if the low point is on your property. If this is not possible I would still go with the drain system on the outside of the foundation but install the sump pump in a catch basin on the outside. It is a very simple job but get several estimates because excavating contractors prices will vary a lot. If your handy just hire a excavator on a hourly basis and do the job yourself. Hope this helps.

Tract0r

If you really need a pump to stay dry put it on a UPS.

I put in the gravel and drains around the basement in my previous home. I also put in a sump pump. It is called a 'french drain'

The development was built on swampland and it was the only system that worked in the homes there.

We put a dehumidifier in the basement.

It was finished with ww carpet and heavily used and we had no troubles.