The argument over who is better Eircell or Esat Digifone I will first note all the good & bad points about the networks & the give you conclusion on what I think.

Esat Digifone

Positive
1. They have the best coverage over all in Ireland covering 98% of the population .
2. They have created a new network from scratch in Ireland which makes it more reliable then     Eircell.
3. They have recently been bought by BTcellnet with means new changes ,cheaper rates like the  ones in the UK
4. They have a great customer care line which will do every possible thing it can do to help you (very nice & helpful caredesk employees)
5. They usual have the best & stylish phones on Speak Easy .
6. There bill phones can opt. for select weekender which allows you to make weekend calls for 2.4p a minute .
7.There network nearly never goes down.
8.You can send sms messages over the net to a Digifone number for free on  sites such as www.mtnsms.com 
9.Digifone are bring out budget phones such as the Motorola L520 for £59.00.
10.You can keep on putting guess' in easy keycards top up service on 1471 (Eircell blocks you from putting in top up numbers after 3 incorrect attempts & you have to ring up customer care to unblock it ).
11. Calls off peak are 10p on weekends to fixed line or 086 & 15p after on week days & 50p peak ,calls to the UK are 75p all the time compared to £1 on Eircell.
12. Speak Easy have Night owl which is 10p weekends & 15p after 6pm on weekdays , Early bird which is 10p weekends & 15p between 8.00 am & 2.00 PM & 50p 2.00 PM to 8.00 AM you can change from plan to plan free every 3 months .
13. Its free to record & listen to your mailbox message 172 , a trick I've done is I record a song I like as my message for my mailbox 172 then if I'm bored I'd ring 172 do listen to current message & listen to the song :-)
14. They support picture messaging on the new Nokia phones Nokia 3210 ,etc.
15. The Digifone Customer Care staff are very well informed in there job & I will do anything possible to help you even call you back & things like this they are more devoted to there job then Eircell's Staff in my opinion .

Negative
1. It doesn't seem you can divert calls from your mobile to another number or use call waiting.
2. You can't roam on foreign networks with your Speak Easy phone. (Put they plan to introduce it in the near future)
3. There information sms services are very limited compared to Eircell .(but have a good wap service which is better then Eircell)
4. They lock some of there phones to Digifone so you cannot put in a different providers simcard unless you  ring in to them & top up to £100
Eircell

Positive
1. There is a vast range of information services by sms such as jokes,horoscopes,etc. .
2. They have plenty of special offers to get people to buy there phones which causes "network busy".
3. The have brought out the Nokia 7110 on ready to go for £350 ,I love the phone but not the price
4. You can send 30 free sms a month off the Eircell website & another 30 off E-merge to other Eircell phones .Very reliable & your phone number comes up so the person who receives it will think you sent it from your own phone the Internet.
5. Eircell has more roaming partners in the world then Digifone.
6. Some times when the networks go down so you can make free calls but watch it they some times deduce the money when you top up your phone I've only heard 1 case of this happening.
7. You can roam on foreign networks with your ready to go.(If you get a roaming contract)
8. The have haft there calls they say 40p peak to other Eircell phones 50p peak to landline or 086 , off-peak 10p to other Eircell phones & 20p to landline & 086 phones .(I think this is miss leading)

Negative
1. They lock there phones to Eircell so you cannot put in a different providers simcard unless you have topped up to £100 & write away to them
2. It is hard to get through to the customer care line sometimes .
3. There customer care people are not as helpful as Digifone customer Care people  & are not given up to date information because most of the are trainees.
4.Their GSM network was built onto there old analogue network 088 so it is not as reliable or efficient as Digifone .
5.They have relatively good reception through out the country.
6. The network is nearly always busy or occasionally down so you can't make a call.
7. They have some numbers barred such as reverse charges which is vital if your car broke down & you have no credit.

Conclusion
So in conclusion it depends on which network gives you better coverage in your area if you live in the countryside but if you live somewhere the coverage is the same I would urge you to get a Digifone mobilephone because they do not bar numbers,give you more for your money,cheaper calls,have over all better coverage,better customer care,usually stylish phones on speak easy & you will never get a network busy message because the are very reliable& the call charges are much cheaper on Digifone speak easy.So forget about Eircell they my try to tempt you with   £50 free credit but once its gone you will start to have problems with the network so buy a Speak Easy Digifone over a ready to go Eircell phone.