Which is better for a half marathon?

The Adios Pro 4. It is far lighter and uses responsive Lightstrike Pro foam built for race pace. The Ultraboost is too heavy and soft for racing.

The Ultraboost. Its everyday build and Boost foam hold up to daily walking and easy runs. The Adios Pro 4 is a race shoe and its foam and upper wear faster with regular training.

Can I use the Adios Pro 4 for daily training?

You can, but it is not ideal. The race geometry and light foam suit fast sessions, and the shoe wears quicker than a daily trainer.

Is the Ultraboost good for running?

For easy jogs and walking, yes. It is heavy and soft, so it is a poor choice for tempo work or long fast efforts.

Which fits wider feet better?

The Adios Pro 4 has a regular fit and is the safer choice for wider feet. The Ultraboost Primeknit sock fit runs snug.

Is the Adios Pro 4 worth stepping up to over the Ultraboost?

Only if you race or train fast on roads. For casual wear and easy days the Ultraboost is the more comfortable, durable pick.

adidas Adios Pro 4 vs adidas Ultraboost 4.0 DNA

These are different tools. The Adios Pro 4 is a carbon-plated-style racing shoe built for speed on tarmac, with a light Lightstrike Pro stack and Continental rubber. The Ultraboost 4.0 DNA is a cushioned everyday sneaker with a Primeknit sock fit and Boost foam, better for walking and casual wear than racing. Buy the Adios Pro 4 for race day and tempo runs; buy the Ultraboost for comfort and daily wear.

Choose the Adios Pro 4 if you race or do tempo runs on roads and want a light, fast shoe with a rockered race geometry.
Choose the Ultraboost 4.0 DNA if you want a soft, sock-fit sneaker for walking, casual wear and easy days.

Prices

adidas Adios Pro 4: $302.00 at Lovell Sports (last seen Nov 9)
adidas Ultraboost 4.0 DNA: $125.00 at Poshmark (last seen Nov 9)
Difference: the adidas Ultraboost 4.0 DNA is $177.00 cheaper than the adidas Adios Pro 4 at the latest prices (Nov 9)