I guess I shouldn't even post here as I haven't even started building yet, but I was on the FKB last night as I am having the same dilemma! I noticed a kitchen that looked very nice and her color on cabinets was BM Linen white. Search Julie Pinkerton's kitchen. Maybe it will help a little. Very pretty kitchen.

The cabinets, trim and wainscoting in my kitchen are BM Linen White. I really love it. I don't know much about BM Mayonnaise though, so I can't compare. My kitchen pictures are in the kitchen blog under Lisa1

If you search either of these colors in the kitchen forum seach, you'll find TONS of previous threads on this very debate.

As for me, I've decided to go with the Linen White. We aren't done yet, but, what's painted so far looks really nice because of the way the color takes on different hues in different lights. In the morning it looks very soft cream; during full sun, it looks bolder cream w/ a hint of yellow(?); at night it's a warmer cream. So hard to describe, but definitely not a stark white, not too grey and dirty, not to yellow, just warm. Let me see if I can find some threads to help you get an idea!

http://ths.gardenweb.com/forums/load/kitchbath/msg0714535215461.html

Not sure if this will be of much help, but my SIL used BM Mayonnaise to paint her kitchen cabs about 6 years ago. To my eye it has gotten more and more yellow and not in a good way. Against the white appliances in her kitchen, the cabs look very "tired". Granted they were old when painted, but she also used it on her trim and her color choices now seem limited to me in other places as a result. JMHO -- good luck.

If you are down to just two colors it would be a good idea to buy a sample (even if that means a quart) and paint a good size area of each in the space you plan to use it. I find it helpful when I paint an edge to touch. Check on the colors throughout the course of several days, hopefully with differing amounts of sun. Don't forget to see how they look at night too.
I was between two different BM whites and this process made it clear that one read too yellow in my space for my taste. Who knows, maybe this is why so many shades of white are available? Either that or they just have a lot of great names they want to use!
I find subtle differences hard to read well on a computer screen. HTH

Thank you for all your help!!!! I have ordered a sample door in each color from Cabico. I tried priming and painting plywood boards in each color, but this is a big investment and I am so afraid I won't get it correct!

Alice462: I am sorry about your SIL's experience with Mayonnaise. I worry about this happening also. My kitchen gets alot of sun. What was the final finish product of the door? Was it a factory finish, or a hand-painted finish? Do you think that maybe it might be worth it to put an addition topcoat on now?

My cabinets are a match to BM Linen White and my trim in the kitchen is BM mayonaise. This should give you a good idea.

This is one of my favorite kitchens from rate my space. She used Linen white for all the trim, looks so soothing. Here is a link.

Here is a link that might be useful: Rate my space LW kitchen