At a glance.

Tesco — biggest national footprint, most competitive when Clubcard is active, strongest food-to-go range.
Dunnes Stores — best-in-class voucher scheme (€10 off €50, every week), excellent own-brand range, the only one of the three with a serious fashion side-business.
SuperValu — strongest on fresh, deli and local producers; Real Rewards programme; often the only full-service shop in smaller towns.

On price.

On a basket of identical branded items, the three are typically within a few euros of each other at list price — Tesco a touch lower most weeks, SuperValu a touch higher, Dunnes in the middle. None of them beats Aldi or Lidl head-to-head on a branded basket, and they don't really try to.

The interesting part is the loyalty / voucher layer on top:

Tesco Clubcard — flat 30–40% off on Clubcard-priced items, week to week. The headline saving on a Tesco shop, if you scan the Clubcard every time.
Dunnes €10-off vouchers — issued on every receipt over €50, redeemable on the next shop. Used consistently, an effective ~20% discount every other week. Save them in Zavvy if you keep losing them.
SuperValu Real Rewards — slower-burn points that convert to vouchers over time. Better if you do nearly all your shopping at SuperValu; less impact if you spread shops around.

On own-brand range.

All three have a "good, better, best" structure:

Tesco — Everyday Value at the cheap end (basics, plain packaging) and Tesco Finest at the premium end (very strong on cheese, ready meals, and dessert). The middle unbadged Tesco range is usually 10–15% under the equivalent branded item.
Dunnes — Dunnes Simply Better is arguably the best supermarket-own premium range in the country: breads, ice cream, deli items, sauces. The middle unbadged Dunnes range is broad and consistent.
SuperValu — SuperValu Signature Tastes at the top, the unbadged SuperValu range across staples. Notably strong on Irish-sourced lines.

On fresh.

SuperValu generally wins here, with the strongest deli, fresh meat counter, and local-producer relationships of the three. Dunnes is right behind on quality across produce and bakery, especially in their bigger stores. Tesco's fresh has improved a lot recently but the lager footprint can mean older stock in smaller locations.

On store coverage.

Tesco has the largest store count nationally with a strong presence in every county. Dunnes is heavily clustered in cities and big towns. SuperValu has by far the deepest village and small-town presence — it's often the only full-service shop in smaller communities, which matters far more than headline price for the people living there.

Which one to pick.

The right answer depends on how you shop:

If you'll commit to one shop: Tesco is likely cheapest with Clubcard active.
If you forget loyalty cards: Dunnes — the vouchers print on the receipt and don't need scanning at the till; you just present them next time.
If fresh and quality matter most: SuperValu, or Dunnes if there's no nearby SuperValu.
If price is everything: none of the three — Aldi or Lidl. See our cheapest-supermarket-in-Ireland walk-through for the bigger picture.

The honest answer for most households is "two of them": one for the main shop (whichever is closest + has loyalty active), and a fortnightly Aldi or Lidl run for the high-leverage staples. See how to cut your weekly grocery bill for the detail.

Tesco vs Dunnes vs SuperValu.