For compound feeds I really like Pure Feeds. They cater for most horsey needs - I have an ulcer prone good doer, so their Fibre Balance is great as it's low cal, low sugar, but has all the mins/vits needed plus biotin, pre and probiotics.
They are very helpful if you call them for advice.
Straights, I've used top chop lite chaff with bailey's low cal balancer, but then added the pre and probiotics separately.
Straights are feeding the feed components separately - so you might choose oats, linseed, maize or peas, herbs, chopped hay etc. (I don't personally count a balencer as feeding straights...) The separate ingredients can be cheaper than the compound feed and you have total control over what is fed. So if your horse is barley sensitive (for example) you don't feed barley. You can tweak the recepie daily. But you do need a lot of feed room space and the ingredients generally come in 20Kg sacks so it can take a time to get through it.
A compound feed is one made by a manufacturer and usually has other stuff as well as the straight ingredients in it - most commonly a vit / min supplement but some have herbs or probiotics etc. If you feed to the a manufacturers guidelines you horse will get all the vits & mins he needs. Compounds can be very high is sugar. Cheaper ones can have neutral bulking agents in them. The expensive ones can (IMO) be a rip off.
Compounds classically come in three forms - a muesli type where you can see all the different bits. A pellet type where the same bits are all there but squashed together in a pellet and a balancer type - which is basically a vit / min supplement in pellet form. Some compound feeds are mixed into a dressed chaff. In straight feed terms chaff (or chop) is just hay or straw you took a pair of scissors to. In compound terms it is dressed with something and may have pellets of compound feed in it.
If you have a number of horses straights are more economical and can be easily tailored. But you do need a fair amount of knowledge and a good source to avoid contamination or a naturally occurring prohibited substance. Compound feeds are a bit more "out of the box" but if they suit they are easier, especially for just one horse. You can get compound feeds certified by BETA as being "NOPS free" - no naturally occurring prohibited substances. Its not an "either / or" either. Many folk (myself included) use compound feeds as a base and add straights. So I use a high quality pellet based compound, add linseed and herbs tailored to each horse and a lo-cal chaff (dressed chaffs are massively high in sugar!). Over the years I've had bran, oats, flaked maize and barley as additional straights.
When I was a girl straights were what was fed, usually bran as a base with oats, cornflakes, peas, barley. The bran was actually likely to upset the calcium/phosphorous balance so was mixed with soaked sugar beet to counter this.
Then along came a compound feed, mostly "Main Ring Red" which was absolutely soaked in sugars, I mean shiny and sticky with the stuff. At the time hard feed recommendations seemed to be very high, as in half a bucket of hard feed was not unusual. It was popular because it was easy, and also the sweet smell appealed to owners, even though it was not generally good for the horses.
Erratic behaviour was made worse by this, so along came "HDF" as in High Digestible Fibre compound products, for me that was Spillars. I went to a talk by Ruth Bishop by Spillars and it was hailed as the new thing. Energy without the sugar highs or high grain.
Later was a "balancer" which would not have been seen as necessary before, as the compound feeds were supposed to have whatever supplementation you needed. But people had realised that, for many horses, the 'recommended feeding amount' was far too high and that hacking a few times a week really only required good quality forage and a token feed, so along came a chaff coupled with a balancer, but the chaffs are still often coated with sugar.
For me I still use what would be seen as a compound feed, but it is an undressed chop type, I use Agrobs Museli, mostly high quality cut grass, but with seeds, beet flakes, carrot flakes, flowers (yes really, but I suspect they are so it looks nice for the owner!).
The trouble with compound feeds is that if your horse is sensitive to one of the ingredients it is difficult to work out which one and to eliminate that one.
Over the years we have fed compound feeds and decided that it is much better (and just as easy) to stick to a very simple diet of single ingredients. Then if there is a problem it is easier to work out which one by a process of elimination. We have had horses which could not tolerate all sorts of things, some quite surprising, and have learned to hard way to keep it simple.
We have mainly had 4 horses though and it is easier to feed straights to multiples, because they don't have the same time to go off, as if you are just feeding one. We are now down to 2 and expect to stick at that and just feed Agros haycobs, linseed, limestone flour Vit E and salt.