COD Warchest is THE premier "you are there" feel WWII FPS compilation ... look no further.
COD excels at portraying large scale engagements and pulling you in with immersive narratives and feel (through excellent graphics and sound). Because of this you really end up feeling like you are part of something big when you undertake the missions in a COD series game. You are always part of a team, albeit you character spends an inordinate amount of time "on point duty" but your AI friends are there to provide cover and move up with you and occasionally even take the lead.
COD also is more global in its outlook in providing British and Soviet campaigns in addition to the requisite American ones. Some of the most intense and brutal engagements occurred on the Eastern Front and the British, for a smaller force pulled above their weight in the North African and Italian campaigns. COD also provides a superior history lesson of WWII in Europe ... there were battles before Kasserine, and indeed other battles equally important as those at Normandy and the Bulge.
On the other hand the missions in MOHAA Warchest are mainly clandestine, behind the lines, with some incongruous returns of the main character to the main US battles of the war like Normandy and the Bulge. But almost always your character will be fighting alone, although nameless friendly AI troops will come and go. Also MOHAA suffers from being overtly US-centric, no doubt the Medal of Honor as a US heroism award limited the options. For me a lone American (in Spearhead) amidst the ruins of Berlin armed with Soviet weapons was just not right. COD at least gets the history mostly right. Eventually the excellent, in under-rated, MOH Pacific would show that history and character development makes for a better experience.
I have recently replayed all three of the COD Warchest games and reviewed each separately at GameSpot and will not go into detail here. Based on my subjective scores for COD (9.0), CODUO (9.0) and COD2 (9.5) I believe the the Warchest compilation rates a 9.5 mainly because, unlike the MOHAA series, each game/expansion is an improvement on its predecessor. This is unlike many series in which subsequent releases, while leveraging off the good name of the original release, are consecutively more disappointing.
COD2 is easily the standout game in the series, albeit the later COD WAW gives it a run for its money in terms of "full on grittiness". Gameplay is slightly improved or enhanced in each game and reaches its pinnacle in COD2 by using a new health mechanic (take cover to heal) and limited (auto) saves and this combination has been retained by COD WAW and COD4 Modern Warfare.
Graphically COD Warchest does not appear to have aged to the degree that MOHAA has. Enemy and friendly AI in the COD Warchest games is consistently good and as realistic as programming human activity probably permits. WWII weapons fans will experience a good range of personal weapons from the American, Soviet and British armouries, most of which appear in their historical context.
Well the realism of COD2's health mechanic is debatable it keeps you engaged in the mission rather than the earlier "hunt for health boxes" system used by COD, CODUO and all the MOHAA series. Likewise COD2's auto save has its critics but allows for a better flow than constant saving (which for example in MOHAA Spearhead was the only way to get through some frustratingly difficult missions). Time spent replaying a mission from the last auto save can occasionally open up new tactical approaches that have a better chance of success. Though sometimes one does wish for the quick save in COD2, but fortunately even the time limited :hold until relieved missions", of which there are several in COD2, do auto save regularly enough.
OVERALL: COD Warchest allows you to enjoy the premier WWII FPS series. Later MOH WWII games, that seem to have cross-fertilised with the COD WWII series, like MOH Pacific and MOH Airborne are among the best newer WWII FPS games available. COD Warchest compilation takes you back to the early years of realistic WWII "historic" shooters and is a good entree before tackling the more recent COD WAW and COD4, which are obvious descendents of COD2.