If there is any chance that you will get water seepage, tile is best. Another possibility is to have the concrete stained.

This depends on various factors such as style options, material cost, installation cost, and finally durability. Both ceramic tiles or porcelain tiles come in unlimited styles, and conversely vinyl tiles also follow suit. This being said choosing one over the other does not limit you from choosing an aesthetically pleasing finish. After this deduction is made we can move on to cost. The cost to purchase vinyl tiles vary depending on the type of vinyl you choose. For example, you may choose between VCT tile or Interlocking vinyl tile. VCT tiles can be purchased generally for less then $1.00 per sq/ft while interlocking vinyl can cost generally $2.50 per sq/ft on the low end. Compared to ceramic or porcelain tiles you will be looking at similar prices although, you will typically be hard pressed to find any decent looking ceramic for less then $1.00 per sq/ft, thus making VCT (Vinyl Composition tile) the most affordable option. When it comes to installation, vinyl tile will be cheaper, and in many cases exceedingly cheaper. When it comes to durability both can be said to be equally durable. VCT tile for instance is extremely resilient to water damage, and additionally it is resilient to cracking. Furthermore, if the finish eventually wears out, it can be re waxed to look brand new. Interlocking vinyl tile is similar in durability although I would suggest that it has a lower lifespan then a properly tiled surface. Also interlocking vinyl tile cannot be renewed after the surface starts to wear over time. Ceramic or porcelain tile on the other hand are also very durable. They share much of the same resiliency as vinyl although they are more susceptible to cracking should you drop a very heavy concentrated weight on it, or if it was not installed correctly, cracking could occur after prolonged use.

In short, considering the fact that vinyl is generally cheaper to purchase, and definitely cheaper to install, and considering its high durability, and resilience, vinyl tile may be the better option. Especially if you are willing to sacrifice on design options, and opt for a VCT tile. With that being said if you can find an aesthetically pleasing ceramic or porcelain tile at an affordable rate, and find a tile setter willing to install it at a reasonable rate or if money is not an option, then tiling the entire basement can prove to be the more attractive option as tile can prove to last decades, and your design options will essentially be limitless.

I have vinyl plank in our walk out basement with Dri core underneath I find it warm easy on the feet and we have dogs in and out of a dog run all day wipes easy no scratches after 8 yrs,

I would say it comes down to where you live and how much standing water you expect to have in your basement on a routine basis.

If you have flooding concerns that pop up on a regular or semi-regular basis than porcelain tile is one of the few finishes that can handle that type of abuse. If standing water is not a concern (it shouldn't be) then vinyl planks, tiles, or sheets can be a very good option in a basement.

If you are in a cold climate, then vinyl is a little warmer than tile....and should be a strong contender.

Vinyl plank/tile will definitely be warmer on the feet, and have a little "softer" feel. An underlayment below the the vinyl can add some insulation as well.

Regarding water/moisture, vinyl can handle anything you throw at it. Of course other materials in the room (walls, frame, subfloor) may develop mold, but you can literally bleach your vinyl planks and still use them even in that kind of worst case scenario.

If you are looking for a wood plank design, vinyl is also much more convincing visually (porcelain/ceramic looks good for stone visuals, but lags vinyl on wood designs). Some factors to keep in mind are the width/length of the planks, and visual details like bevels, which all contribute to a more convincing product. Here are some examples of vinyl plank:

http://www.flooret.com/modin-vinyl-plank-flooring/

Barin Vinyl Plank · More Info

Imber Vinyl plank · More Info

Maltan Vinyl Plank · More Info