Let me gather data on all three archetypes across the relevant formats to give you a data-backed answer. Let me start by identifying the format and pulling meta reports.
Jeskai Control appears in Pioneer and Dimir Midrange in Standard. Let me check if the user means Standard (where Dimir Mid is dominant), search for 4-color control in Standard, and pull the relevant matchup and winrate data.
The Standard meta has Jeskai Control, Dimir Midrange, but no "4 Color Control" showing up. I see "Jeskai Lessons" which might be what the user calls Jeskai Control. Let me check the Standard meta for any 4-color archetype and get the key matchup data. I also notice Jeskai Lessons is distinct from Jeskai Control in Standard. Let me pull matchup data for both Jeskai variants vs Dimir.
Both Jeskai variants struggle vs Dimir. Let me look more broadly for a 4-color archetype in Standard and also get the matchup data vs Dimir Excruciator (likely a Dimir variant too) and look at the full meta more carefully.
Interesting! Jeskai Lessons beats Dimir Excruciator but struggles vs Dimir Midrange. Let me now check both Jeskai archetypes against "5c legends" (the most common 4+ color archetype), and also look at the broader "4 color" archetype search more carefully.
Now I have a clear picture. Let me get the Jeskai Lessons winrate vs Dimir Midrange (the key matchup) and get sources to cite. The data shows Jeskai Lessons is the Standard version and is clearly performing better overall. Let me note that "Jeskai Control" in Standard appears to be a very small sample (Pioneer archetype bleeding into results). The true Standard "Jeskai" deck is Jeskai Lessons.
Now I have everything I need. The question is clearly about Standard (where Dimir Midrange is the big deck). The relevant "Jeskai" deck in Standard is Jeskai Lessons, not Jeskai Control. Here's the full picture:
The question is about Standard. In that format, the relevant Jeskai archetype is Jeskai Lessons (the Jeskai Control name mostly tags Pioneer entries). Neither version is a great fit for a meta heavy on Dimir, and here is why.
Jeskai Lessons vs the two named threats, based on the last two months of Standard data (179 entries, 51.1% overall winrate excluding mirrors):
vs Dimir Midrange: Jeskai Lessons goes 2-8 (20.0% winrate). This is a brutal matchup. Dimir Midrange's proactive threat density with Kaito, Bane of Nightmares backed by disruption runs right over the Lessons gameplan.
vs Dimir Excruciator: Jeskai Lessons goes 37-25 (59.7% winrate). This is actually a strong positive matchup, so if "Dimir mid" refers to Excruciator lists, the picture is more favorable.
vs the closest 4-color archetype (5c Legends, which is the only multi-color non-Jeskai control shell with real volume): Jeskai Lessons goes 5-6 (45.5%), roughly even. This matchup is not a strong point either.
The honest data answer is that neither Jeskai build is well-positioned in a meta dominated by true Dimir Midrange specifically. If your local meta is heavy on Dimir Excruciator-style decks, Jeskai Lessons is the pick (nearly 60% in that matchup). If it is pure Dimir Midrange (Kaito builds), tournament data suggests you are walking into a 20% matchup and should look elsewhere. There is no 4 Color Control archetype in Standard with enough volume to draw firm matchup conclusions - it registers only a handful of entries.
Sources: Data from 56 Standard tournaments over the last 60 days, 84% MTGO and 16% Melee.