I do think that DME is more expensive even if you take into account that you use less DME than LME, but some people can taste a twang when they use LME that is old, especially when they put it in at the beginning of the boil. A couple other disadvantages are that it can sink to the bottom of your pot easier and scorch and also some people report that LME doesn't ferment down as completely as DME.
I'm new to the home brew experience.....but I have been burned using LME the two times I have used it. I bought kits online that come with LME (White House Honey Porter and a Saison) and in both instances I got the same "twang" in my beer which made me pour them down the drain. I took both beers to my local home brew store and they believed that the result of the "twang" was oxidized LME. I haven't experienced any of these problems with DME.
A partial-mash approach could be a good idea - it reduces the amount of DME and therefore the cost and also allows you to increase the depth and flavor profile of your beer.
Just quickly looking at a couple of the big vendors it looks like DME and LME are pretty comparable in price when you figure in the conversion factor (you need about 1.25 x the amount of LME for DME). Except for those few specialty extracts like MO or Munich that I haven't seen offered as dry I'd definitely go all DME if I was still brewing extract.
Heat and age affect malt extracts, but LME usually darkens and takes on a twang much sooner than DME. If you ever plan to buy in bulk or stock up during a sale, I'd look at DME. Store it in an airtight container somewhere cool and dark to keep it fresh.
The only LME I ever used was with Northern Brewer kits. I feel that the LME was very fresh and my beers did not get the dreaded "twang". If you buy a box off the shelf somewhere, you really don't know how long it sat there. I suggest online ordering of kits that the store sells. Not one where the store buys kits from a company wholesale then sells them retail. That adds to how long between the manufacture and your brewday.
I to prefer DME. I keep some on hand for yeast starters, gravity adjustments and the rare occasion that I brew and extract batch.
Yes, Briess LME does have a date you can see to judge the age of the product. If you look on the bottom of a 3.3lb container of unhopped LME there are two lines of information
The second line is the month/day/year of packaging, followed by time.
160116BR1 (Bavarian Wheat)
020916 14:11 (Feb 09, 2016 2:11PM)
This particular code is on a Briess LME container I have right now and will use soon. It's just over a year old, gotta hop on it.
1) DME should be slightly cheaper.
2) I can't taste the difference.
3) I use mostly LME because I cannot seem to use DME without making an unpleasant to clean mess. That's the only reason I have to use LME, but it's a big enough reason for me.
4) When using LME, I use the entire container, adding DME for amounts less than the next LME container. I use up to 6 lb of grain, so that means I use DME only when I'm brewing a big beer, or those where there is not a comparable LME for the DME.
4) I am willing store a partial bag of DME, but not a partial LME containers.